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## Battery Weight V.S. Acceleration Time

## Battery Weight V.S. Acceleration Time

Submitted by BladeRunnings on 25. Februar 2011

Is it safe to assume that there will be a weight difference between the 160, 230, and 300 mile range battery packs? If so, what will this do to the overall acceleration of the car? The website shows that the Model S will hit 60mph in about 5.6 seconds and can have a range of 300 miles. Could this possibly mean that if one were to purchase a Model S with the 160 mile pack that it may accelerate to 60mph closer to or even under the 5.0 second mark due to less weight? Or do you think that Tesla based their approximate acceleration statistic on the lighter battery pack?

Brian H| 25. Februar 2011Sounds reasonable.

William13| 26. Februar 2011Smaller battery pack equals less available power which unfortunately will more than offset weight loss. The smaller pack with current batteries will not accelerate as quickly.

BladeRunnings| 26. Februar 2011It will be nice if they based their acceleration approximation on the 160 mile pack in that case. I really hope they didn't base it on the 300 mile pack especially since, from what I understand, that battery won't even be available when they start production.

ggr| 26. Februar 2011William13, I don't think you are correct. The smaller pack won't be able to supply the power for as long, but it should be perfectly capable of delivering the same peak power (subject to stuff like overheating). So with less weight, for a short time, it will perform better because of lower weight.

Greg.

Timo| 26. Februar 2011Odd, I'm sure I posted here numbers based on assumptions and my post has disappeared.

Short version: estimated weight: 4000lbs, 0-60 5.6secs 160mile pack.

F=ma F is constant m varies by 100kg need to solve a from one side of equation. Result: 230 mile pack around 5.9 secs.

I believe that 5.6 is based on 160 mile version, 230 and 300 mile versions use same amount of cells, different chemistry. Model S battery is probably lighter than Roadster battery thanks to it being part of the structure.

MODERATOR: did my post get deleted for some reason? It should be right after Brian H "Sounds reasonable" -message. If so why? If it never appeared here (can't really remember) I don't know what happened.

Brian H| 26. Februar 2011Timo;

You probably used one of the secret forbidden number combinations. I can't give you the list because it would probably delete the whole thread, or even the whole forum, of course.

;)

>:p

William13| 27. Februar 2011I thought that in one of the engineering videos that they said with the model s motor that the 160 mile version would not have sufficient amperage to reach maximum acceleration. The model s motor is significantly larger than the roadster motor with corresponding higher power requirement. The 160 mile version has same amount of available battery power as the roadster. I think someone mentioned that the motor could draw more. This would imply the PEM would prevent max acceleration to protect the batteries.

BladeRunnings| 28. Februar 2011I was kind of hoping for something that could hit 60mph in under 5.0 seconds. ;)

Volker.Berlin| 28. Februar 2011I was kind of hoping for something that could hit 60mph in under 5.0 seconds. ;)

Roadster 3.9 seconds, Roadster Sport 3.7 seconds.

BladeRunnings| 01. März 2011I would love a Roadster! It's quite a bit more than I can afford at this point in time though. I heard 2011 is the last year they will be producing the current Roadster models. I've also heard that they will be bringing back a re-designed model in 2013. That seems like such a short period of time to re-design the car though. Do you guys think it's possible?

Volker.Berlin| 01. März 2011According to Tesla's latest Newsletter (28-Feb-2011):

Responding to international demand, Tesla has increased Roadster production by 100 vehicles. In total, 2,500 cars will be produced. Although demand exceeds 2,500 vehicles, Tesla will stay true to its original commitment that the Roadster's limited production will help make it a collector's item. The order increase allows Tesla to respond to market demand in 2011 and 2012 while maintaining exclusivity.

To me, "maintaining exclusivity" and "collector's item" does not sound like they are eager to offer a similar model soon.

ckessel| 01. März 2011Even at 5.6, the Model S is very comparable with the top speedsters in it's class. I'd imagine the sport model would get pretty crazy quick for the class, but it'll be a bit longer before that's available.

BladeRunnings| 01. März 2011According to the article at: http://venturebeat.com/2010/03/29/tesla-extends-roadsters-lifespan-with-... written on May 29, 2010:

After the sedan [Model S] has some time to penetrate the auto market, Tesla plans to bring the Roadster back — with some modifications — by 2013 or 2014.

Is this no longer the case?

BladeRunnings| 01. März 2011ckessel,

A 0-60 mph acceleration time of 5.6 seconds is definitely impressive for a car the size of the Model S. Eventually I'm hoping to test drive and possibly purchase one. My current car can hit 60 mph in about 5.3 seconds, weighs 4465 lbs, can travel about 300 miles per tank of ridiculously over-priced (and always rising) gasoline, and cost me about $30,000 back in 2004. I'm kind of hoping that Tesla will eventually come up with something that's at least a bit faster than my current car that can also travel at least 250 miles on a charge and cost under $60,000. Perhaps the sport version will be something similar? I kind of doubt it will be less than $60,000 though. My car currently has nearly 115,000 miles on it and I've spent a total of about $53,000 on it since I bought it. This cost includes the initial cost of the car, gasoline, repairs, and maintenance.

Brian H| 01. März 2011BladeR;

Lots of those dollars are 7 years old, of course, and are worth rather more in inflated 2011 bux! I'd say you could add $15K or so to that total in current currency. ;)

msiano17| 01. März 2011@Blade

Your total cost of your car is astounding and excellent reasoning to transfer to a EV low maintenance vehicle ... $83,000 in 7 years ... expensive

Volker.Berlin| 02. März 2011We are all getting too used to the insane numbers of the Tesla Roadster, and obviously 5.6 looks rather mediocre in this comparison. I would like to put things back into perspective: The Model S is not so bad after all. :-)

A perfectly normal modern family car with comparatively low fuel consumption needs in the order of 9 to 12 seconds to get from 0 to 60 mph. Obviously, the Model S plays in a totally different league.

Premium sedans bring down that number to something like 7 or 8 seconds. These cars have reasonable fuel consumption and are very comparable to the Model S in terms of price, size and "class", but still no match for the Model S when it comes to acceleration.

Then there are high-end performance cars. They are really expensive (much more than the Model S), typically have 6 or 8 cylinders and burn fuel like crazy. Acceleration-wise, those are the cars the Model S compares to and it holds up against them pretty well. The Model S accelerates as fast as a Porsche Panamera S! No surprise some of these cars accelerate even faster, but it takes another order of magnitude (in terms of money and fuel consumption) to keep up with the Roadster.

Here are some figures from the web. I did not even bother to mention the cars that have the greatest volume in terms of sales (the Toyota is just a representative for these models). I focused on the models you probably dream of, and which you want to beat at the stop lights... ;-) Nota bene: Some of them cannot even seat 4 passengers!

Toyota Avensis 2.0: 9.0

BMW

320i: 8.2

335d: 6.0

335i: 5.6

523i: 9.0

535i: 6.0

550i: 5.0

M3: 4.9

M5: 4.7

Mercedes

E 200 CGI: 8.5

E 350 CGI: 6.8

E 500: 5.2

S 350: 7.3

S 450: 5.9

S 500: 5.4

S 600: 4.6

Audi

A4 2.0 TFSI: 7.9

S4: 5.1

A5 3.2 FSI: 6.1

S5: 5.1

A6 2.8 FSI: 7.7

TT 2.0 TFSI: 6.1

TT RS: 4.6

R8 5.2 FSI: 3.9

Porsche

Cayman: 5.8

Cayman S: 5.2

911 Carrera: 4.9

911 GT3: 4.1

911 GT3 RS: 4.0

Panamera: 6.8

Panamera S: 5.6

Aston Martin

V8 Vantage: 4.9

Rapide: 5.2

Tesla

Model S: 5.6

Roadster: 3.9

Roadster Sport: 3.7

One last remark: When the Model S production is up and running and selling well, I fully expect Tesla to bring a sports version of the Model S, comparable to BMW's M-series or Audi's S-series. There is still room for even better performance.

Nicu| 02. März 2011Some wild speculation, that I posted on Traderhood

http://www.traderhood.com/2011/02/19/tesla-er/#comments

We know that the 300mi range battery has the same number of cells (8000) as the 230mi one. Just different chemistry / structure inside cells. So we may assume they also have higher power density, not only energy density. As they can be charged in 45 min. to 80% capacity, all models should be quite high power both ways. The 5000 cells battery can achieve 0-60mph in 5.6s.

So where I want to come to is the following : the 300mi pack should have about twice the power (and energy) than the 160mi one. Add a second motor for AWD and you get a sport version with double the power and torque. It is slightly heavier (100-150 kg) so instead of 5.6s/2 = 2.8s, you get 3s for 0-60mph !

I know it sounds crazy, but for $10k-$15k extra for the end user, you get a family car that beats all Ferraris, Lamborghinis, Porches, Jaguars … you name it ! You can count on your fingers the cars getting under 3s for 0-60mph, we are talking about real super car beasts here !

Of course they could not sell Roadsters anymore if they announce this Big Boy. But they plan to stop production this year and sell the stock by the introduction of the Model S anyway !

So I guess we have to wait at least one year to check how far from the truth I am. Of course, if the sports model does not have two motors, just a slightly modified one, none of this is even close.

I would add that they also have hinted at an AWD, and it makes no sense to build a complicated transmission which would be as heavy as a second motor (and a bit of extra cables + software) – and inefficient. As the battery occupies the floor of the car, the transmission would also modify the chassis. And there is a trunk in front, just use a quarter of it for the second motor (+ PEM + the small gearbox).

Timo| 02. März 201145 minutes to 80% of 100kWh battery pack is only 106kW, and I believe 100kWh is overestimate of battery size. Both Roadster and Model S engines can draw over 200kW. Considering that is already twice the capacity it is quite good power density. Putting in second engine probably can't get double power from same package.

Volker.Berlin| 02. März 2011Fun idea, albeit your calculation is a little naive. Acceleration does not go linear with Power:

318i / 105 kW / 9.1 sec

335i / 225 kW / 5.6 sec

M3 / 309 kW / 4.9 sec

523i / 150 kW / 7.9 sec

535i / 225 kW / 6.0 sec

550i / 300 kW / 5.0 sec

911 Carrera / 254 kW / 4.9 sec

911 GT3 RS / 331 kW / 4.0 sec

You see what I mean? If the relation was linear, the 335i would jump to 60 mph in 4.6 seconds, based on the 318i data, and the 550i would be a 4.0 rather than 5.0 based on the 523i.

So yes, it is probably possible to accelerate the Model S a lot faster than the first version will be able to go, and going AWD probably helps not only to get the required traction, but also by adding up the power of two motors. But I doubt that a car the size of the Model S will accelerate in 4 seconds or less for any reasonable amount of money.

Nicu| 02. März 2011it's double power, double torque, double traction (wheels to ground) :)

and a bit of extra weight; also there is enough weight on front wheels to get good traction from the battery and extra motor

and yes, the charging time was probably a bad example, but usually power in is much lower than power out; maybe the better way to compute is 8k cells instead of 5k cells + better chemistry

Nicu| 02. März 2011oh, and there's no stupid gearbox to lose time changing gears (+ lost efficiency) and tight RPM windows where you get maximum power and torque

in the ideal situation, double force for the same amount of mass means double acceleration which is half the time to accelerate to the same speed (speed is the integral of acceleration and the integral operator is linear :p )

so I speculate that double torque, double power and double traction (from 0 RPM with no gear changes) amounts to about double the force exerted on the car - of course the main question is the battery and there are several other minor questions (e.g. does momentum reduce the traction on front wheels ? if so, by how much ? etc.)

MikAo| 02. März 2011http://www.greencarcongress.com/2009/12/panasonic-20091225.html

It seems not to be big difference in weight of 230 mi and 300 mi batteries compared to 160 version (current)if number of cells is the same. +20 % is safe assumption between the last two.

Nicu| 02. März 201146g-44g = 2g seems more like 5% :) - but of course one should also add at least 150kg for the extra 3k cells

so you get a car that is about 15% heavier; so in an ideal world you get 3.2s 0-60mph time - no other family car could ever dream to approach this !

I'm assuming that they use 3.4Ah in the 300mi pack - anyway, we have no info about that, the cell design might have changed by now

Volker.Berlin| 02. März 2011in the ideal situation, double force for the same amount of mass means double acceleration which is half the time to accelerate to the same speed

Right. In the ideal situation, there is also no air or tire resistance, and infinite traction. Well... infinite traction is probably hard to achieve with zero tire resistance, and I am not sure if I would consider a world without air "ideal". ;-)

qwk| 02. März 2011There is no way Tesla is going to make a Model S 0-60mph time around 3 seconds.

Not only is the power v.s time not linear, a car with that capability would scare most drivers. This is a no go from a safety standpoint for a family sedan.

Nicu| 02. März 2011scared drivers will choose the "normal" Model S :)

Volker.Berlin| 02. März 2011Not only is the power v.s time not linear, a car with that capability would scare most drivers. This is a no go from a safety standpoint for a family sedan.

They could use a special Top Acceleration Key, as is used for the Bugatti Veyron to unlock it's top speed ($2.7 Mio, 2.5 sec 0-62 mph, 883 kW, 430 kmh/267 mph top speed). ;-)

BladeRunnings| 02. März 2011msiano17,

I haven't paid $83,000 for my current car overall. I've paid $53,000 which includes the initial cost. Here's a bit of a break down:

Initial Cost: $30,000 in 2004

Starter replacement at about 80,000 miles: $700

Water pump replacement at about 85,000 miles: $300

Radiator replacement at about 95,000 miles: $200

Clutch replacement at 100,000 miles: $2,300

Oil changes over 6 1/2 years (synthetic): $1,820

Gasoline over 115,000 miles (average 20mpg, $3/gallon): $17,250

This comes out to $52,570 which I rounded up to $53,000 for miscellaneous things that I'm sure I've overlooked. Do you guys see anything that I may have missed?

BladeRunnings| 02. März 2011I also have a hard time thinking that Tesla will produce a Model S that is capable of super car acceleration times. It would be awesome if the released one that could compete with the Subaru STI and similar cars though I wouldn't consider cars like that in the family class.

Volker.Berlin| 02. März 2011For the record:

Subaru WRX STI: 221 kW / 5.2 sec

Nicu| 02. März 2011that is what new tech may enable :)

think that in the car industry the power increased in 100 years by a factor achieved in computing in less than 10 years; electric motors may just give us a quantum leap !

Ramon123| 02. März 2011There's an enormous amount of speculation here based on

very sketchy information. As I recall, the 300 mile battery pack

contains advanced high density batteries. I assumed that the weight of the 300 mile pack would equal that of the 240 mile pack, which will be greater than the 160 mile packs, presumably by roughly 50% (excluding common weight, such as the enclosing metal

envelop, coolant, etc. ). I don't believe that Tesla specifically indicated which battery pack produced the estimated 5.6 second acceleration time. Perhaps it's essentially the same for all three. Obviously a larger battery pack could provide more power, but perhaps the smaller packs can provide just about all the juice the motor could ever consume, and while the larger packs can provide somewhat more, they are also heavier. Notice that the Fisker Karma, using only its small battery pack (probably around 16kWhrs), cannot accelerate faster than 8 seconds, but by running its engine in addition, can get to around 6 seconds. The Fisker weight is said to be 1000 pounds more than the Model S. But if that pack were as large as the 160 mile Tesla pack (around 40 kWhrs) it obviously wouldn't need to turn on the gas engine to generate enough power. This data leads me to believe that the 5.6 second time is probably for the base battery pack option and it's likely that the longer range models don't differ substantially.

A better approach would be to simply ask Tesla engineers. They'll know.

Roblab| 03. März 2011To add fuel to the fire of rampant speculation: I heard or read somewhere, don't remember or I'd post link, that the S super will go 0-60 in 4.4 sec. Dream on, my friends!

Volker.Berlin| 03. März 2011I heard or read somewhere, don't remember or I'd post link, that the S super will go 0-60 in 4.4 sec.

This seems to be a popular rumor, 1st hand sources that confirm these numbers would be very welcome. As far as I am concerned, 4.4 seems a plausible figure for a Model S Sport.

qwk| 04. März 2011The Model S sport is supposedly going to have a 4.4s 0-60. That is probably as good as it's going to get for the 4 door model s.

Nicu| 06. März 2011OK, let's come back in about one year (or when Tesla announces the sports Model S) to see what gives. My prediction remains that AWD implies under 4s 0-60mph, possibly under 3.5s !

Ad van der Meer| 06. März 2011Now seriously! 0-60 under 4 s or even 3.5s?

The standard Roadster does 0-60 in 3.9, the Sport in 3,7.

The standard Model S will do 0-60 in 5,6s. To make the Model S Sport do anything near 4s would take quite a leap from the standard model. Since the weight will not change substantially, it will require serious extra power.

It takes a Maserati QP 295kw to get to 60 in 5.6s and the QP GTS 325kw to get there in 5.1s.

Anything under 5s for the Model S Sport would be a very nice accomplishment IMHO.

searcher| 06. März 2011Careful with all that street racing folks.

Timo| 07. März 2011It is not power that accelerates a car, it is the torque. That is why Roadster beats cars with twice the power in short drag races even that it isn't lightweight car.

If you double the torque you accelerate twice as fast, assuming you can actually deliver that torque to the ground. Problem is that with that much weight normal tires start to slip before you get the acceleration anywhere near under 4 seconds and all you get is a lot of smoke and burned tires.

OTOH with a lot more torque available you can change gearing for a lot higher top speed without sacrificing acceleration. Car that delivers same torque at 0 that can make tires slip and continues to deliver that same torque to the ground at 60 will burn rubber in 60 if you floor the accelerator.

qwk| 07. März 2011Timo, that is a very common misconception. Hp is derived from torque.

While torque does help cars get off the line, ultimately if your vehicle does not have much hp, it will be slow.

A very good example; there are 500whp/200wtq imports that will destroy 200whp/500wtq v8 cars.

Nicu| 07. März 2011well, I explained earlier how that could be obtained, assuming the battery is powerful enough :

two motors, so we have double power, double torque, double tire surface (traction) :)

Ad van der Meer| 07. März 2011The Maserati QP S and the GTS have the same torque, but the GTS is 0,3s quicker to 60mph, but hey I'm no engineer (unlike some others here). Please educate...

All I know is that when you press the pedal on the right you go faster... and when pressing the pedal on the left doesn´t slow you down, you´re in trouble...

Timo| 07. März 2011@qwk, torque is direct force that accelerates the car. It is torque that accelerates things. At zero RPM you have zero HP, yet you accelerate. Power doesn't tell the acceleration, it is torque. Directly at tires, with gear ratios used at motor.

Power OTOH does tell the top speed you can achieve (well, maybe, assuming you can hit the top power at the top speed RPM). Low power car is not very fast.

@Nicu, double traction doesn't apply in 4WD, when accelerating rear tires get a lot more traction than front tires. When accelerating really fast front tires may even get airborne.

@Ad van der Meer, GTS has probably a bit shorter gearing or it changes gears that 0.3 second faster (if it is necessary in 0-60, not all ICE cars need gear changes in that).

Nicu| 08. März 2011Yep, I admitted there could be a bit less traction on front wheels but we have to remember that the battery is heavy and the center of gravity is very low (plus extra motor on the front wheels); it may be true that up to 20mph front wheels contribution may be small, above that it's only power an torque that matter.

So I'm not claiming the theoretical 3.2s (estimated from 2x everything plus 300kg for the larger battery and extra motor / PEM / "gearbox"), but only 3.5s-4s !

VolkerP| 08. März 2011Timo, Ad, both of you are correct in some way.

Let me try to clear up with some physical background.

Torque is translated into acceleration force by the wheel diameter. Thus, more torque=more acceleration.

Power delivered by the engine is proportional to torque multiplied by RPM.

Neither torque nor power are constant over RPM for any given engine, be it ICE or electric motor (see http://www.teslamotors.com/roadster/technology/motor)

For the first few meters, acceleration is limited by tire grip. That's where traction control cuts in to limit engine power, thus limiting torque. usually, you reach ~1g in the beginning for supercars.

Power needed to accelerate a mass is product of speed x mass x acceleration. Assuming a car mass of 2000kg, acceleration 10m/s², we achieve 10m/s after 1s. We need 200'000 kg m²/s² = 200kW (in SI units) to sustain that acceleration at that point of time. Power lost to drag is neglected here!

10m/s equals 22mph or 36kph, and 200kW equals 268hp.

Constantly accelerating to 27m/s (=60mph) we come out at 540kW = 724hp. Somewhat earlier will be the point where we run out of engine power to keep up that acceleration. The traction limit on acceleration is replaced with a power limit. Assuming constant power delivery by an electric motor, this results in a differential equation to which I haven't looked up the solution yet. For ICE car it is way harder to predict because of it's narrow ideal RPM range.

EV will win drag race over ICE in torque limited acceleration phase. ICE will win in power limited acceleration phase IF it is capable of making up the losses at the start.

And for Model S to reach 4.4s for 0-60mph: I guestimate that a drivetrain in the 400kW area will be needed for that.

gianni.terragni| 08. März 2011I reserved a model S.After your interesting discussion about acceleration, that shows a good knowledge of phisic laws, both theoretical and applied, I hope Tesla will sell me a car, not a dragster

Volker.Berlin| 08. März 2011I hope Tesla will sell me a car, not a dragster

The short answer is: Both. :-)

Vawlkus| 08. März 2011The better answer is: only if you drive it that way.

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